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NCERT Class XI Chemistry Thermodynamics Solutions

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Question : 10 of 22
Marks: +1, -0
Calculate the enthalpy change on freezing of 1.0 mol of water at 10.0°C to ice at –10.0°C. ΔfusH\Delta_{\mathrm{fus}}H = 6.03 kJmol1\mathrm{kJ\,mol}^{-1} at 0°C, CP[H2O(l)]\mathrm{C_P[H_2O_{(l)}]} = 75.3 Jmol1K1\mathrm{J\,mol^{-1}\,K^{-1}}, CP[H2O(s)]\mathrm{C_P[H_2O_{(s)}]} = 36.8 Jmol1K1\mathrm{J\,mol^{-1}\,K^{-1}}.
Solution:  
The enthalpy change on freezing from 10°C to –10°C may be expressed as
Liquid (10°C) ΔH1\xrightarrow{\Delta H_1} Liquid (0°C) ΔH2\xrightarrow{\Delta H_2} Solid (0°C) ΔH3\xrightarrow{\Delta H_3} Solid (–10°C)
ΔH1\Delta H_1 = nCp[H2O(l)]n\mathrm{C_p[H_2O_{(l)}]} × ΔT = 1 × 75.3 Jmol1K1\mathrm{J\,mol^{-1}\,K^{-1}} × (–10)
= –753 Jmol1\mathrm{J\,mol}^{-1} = – 0.753 kJmol1\mathrm{kJ\,mol}^{-1}
ΔH2\Delta H_2 = n(ΔfusH)n(-\Delta_{\mathrm{fus}}H) = –1 × 6.03 = –6.03 kJmol1\mathrm{kJ\,mol}^{-1}
ΔH3\Delta H_3 = nCP[H2O(s)]n\mathrm{C_P[H_2O_{(s)}]} = –1 × 36.8 × 10 = –368 Jmol1\mathrm{J\,mol}^{-1} = –0.368 kJmol1\mathrm{kJ\,mol}^{-1}
ΔH = ΔH1+ΔH2+ΔH3\Delta H_1 + \Delta H_2 + \Delta H_3 = – 0.753 – 6.03 – 0.368 kJmol1\mathrm{kJ\,mol}^{-1} = –7.151 kJmol1\mathrm{kJ\,mol}^{-1}
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